The first obvious answer is look at the dimensions of the other one and dimension this one accordingly.

Ok, that's probably not what you were looking for. :-) If you have both parts in an assy, you can edit the desired part there. If you have the setting set to not allow external references, then you can reference that other hole but it will not "stick". This lets you place it relative to the existing hole, then open that new part and put dimensions on the new hole.

Now I have another problem. I want to use the Hole Wizard to put tapped holes in a base plate within an assy. I want to use the existing holes in a mated plate for location reference. When I select the plate face for the hole, an unwanted hole appears. When I delete it, all the holes are deleted also.

It sounds like you are on a version before 2012. When you select that face, then what you see is that extra hole location. Just continue to place the other points where you want them and then delete that extra point. It should work fine like that.

That's odd because I just tried it on 2011 and when I delete that first sketch point while in the Positions tab of the Hole Wizard, that point disappears and the other points are still there just fine. Are you doing it like that?